Making Triangles

Date: 11/12/2001 at 14:29:56
From: David
Subject: Demonstrating triangles
I've been trying to find ways to demonstrate a triangle that contains
180 degrees without using a protractor.
-Dave

Date: 11/12/2001 at 15:50:27
From: Doctor Peterson
Subject: Re: Demonstrating triangles
Hi, David.
Here's a simple way to demonstrate what you want. Three angles that
add up to 180 degrees can be put together to form a straight angle (a
line):
\ /
\ /
a\b/c
------+------
So make a triangle out of paper, tear off the three corners, and fit
them together this way. They should always form a straight line.
Or, to make a more impressive demonstration that comes close to a
geometrical proof, place your triangle so that angles a and c are both
acute (b may be obtuse), and fold the corners in (dividing two edges
in half) so they all meet on the remaining edge:
+
/ b \
/ \
/ \
/ fold \
+-------------------+
/|f f| \
/ |o o| \
/ |l l| \
/a |d d| c \
+----+-------------------+--------------+
+-------------------+
|\ / |
| \ / |
| \ / |
| a\ b /c |
+----+--------------+
You will end up with a rectangle surrounding three angles that
together form its bottom edge: 180 degrees.
- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/